Finite Element Analysis for Machine Design
This course introduces classical and modern techniques for the analysis and design of electromagnetic devices such as electric machines and transformers. Emphasis is placed on finite element analysis (FEA), winding analysis, and magnetic material modeling. Students apply electromagnetic theory to practical design problems using commercial simulation software.
Objectives
- Classify electromagnetic partial differential equations and apply appropriate boundary conditions.
- Apply electromagnetic field theory concepts including magnetostatics, quasi-statics, and magnetic scalar potential.
- Formulate electromagnetic problems using variational methods and weighted-residual approaches.
- Implement the finite element method, including shape functions and step-by-step solution procedures.
- Model permanent magnet materials and represent them using equivalent magnetic circuit models.
- Analyze electrical windings using turns functions, winding functions, and distributed winding theory.
- Evaluate winding factors, fractional-slot and concentrated winding configurations, and slotting effects.
- Apply Carter’s coefficient and star-of-slot analysis in electric machine design.
- Solve practical electromagnetic design problems using commercial finite element analysis software.
- Analyze and design transformers and permanent magnet machines under voltage and current constraints.
Textbooks
Electromagnetic Modeling by Finite Element Methods
J. P. A. Bastos, N. Sadowski · Marcel Dekker (CRC Press)
Electrical Machine Analysis Using Finite Elements
N. Bianchi · CRC Press
Variable Speed Generators
I. Boldea · CRC Press
Permanent Magnet Motor Technology: Design and Applications
J. F. Gieras · CRC Press
Permanent Magnet Synchronous and Brushless DC Motor Drives
R. Krishnan · CRC Press
Introduction to AC Machine Design
T. A. Lipo · University of Wisconsin Publication (Wiley)
Finite Element Analysis of Electrical Machines
S. Salon · Springer
Numerical Techniques in Electromagnetics
M. N. O. Sadiku · CRC Press
Modules
Description: Introduction to Finite Element Analysis (FEA) for electric machines, covering the scope of the course and the role of numerical methods in electromagnetic design.
Description: Continuation of the introduction, setting up the mathematical framework for solving electromagnetic problems using FEA.
Description: Review of Maxwell's equations as they apply to low-frequency magnetic problems and the definition of boundary conditions.
Description: Deep dive into differential equations used in FEA, specifically focusing on the magnetic vector potential formulation.
Description: Fundamentals of meshing and discretizing the domain into finite elements to solve partial differential equations.
Description: Advanced meshing techniques and the impact of mesh quality on solution accuracy and convergence.
Description: Solving magnetostatic problems where material properties are linear, focusing on air gaps and core materials.
Description: Practical examples of linear magnetostatic simulations and analysis of flux density distribution.
Description: Introduction to nonlinear magnetic materials, B-H curves, and modeling magnetic saturation in electrical steels.
Description: Newton-Raphson methods and iterative solvers for handling nonlinear material properties in FEA.
Description: Techniques for modeling permanent magnets (PM) in FEA, including remanence and coercivity definitions.
Description: Simulation of PM machines, setting magnetization direction, and analyzing the operating point of magnets.
Description: Introduction to eddy currents, skin effect, and time-harmonic (AC) solvers for steady-state analysis.
Description: Loss calculation in conductors and laminations using AC magnetic simulation.
Description: Setup for transient solvers to analyze time-stepping phenomena, motion, and dynamic performance.
Description: Coupling motion with magnetic fields to simulate rotating machines and torque production over time.
Description: Methods for calculating electromagnetic forces and torque, including the Maxwell Stress Tensor and Virtual Work method.
Description: Analyzing torque ripple, cogging torque, and optimizing geometry to minimize vibrations.
Description: Defining coil terminals, winding phases, and linking external circuits to the FEA model.
Description: Advanced circuit coupling, including diode rectifiers and inverter switching effects in FEA.
Description: Theoretical background of core losses (hysteresis, eddy, excess) and the Bertotti model.
Description: Applying core loss coefficients in FEA software and interpreting loss density maps.
Description: Introduction to Multiphysics: coupling electromagnetic losses to thermal solvers.
Description: Setting up thermal boundary conditions and steady-state thermal simulations for motors.
Description: Advanced topics in machine simulation, potentially covering 3D effects or specific machine topologies.
Description: Case studies and problem-solving sessions using commercial FEA software.
Description: Focused analysis on specific design challenges, such as demagnetization analysis or fault conditions.
Description: Continuation of special topics, analyzing harmonics and parasitic effects.
Description: Strategies for using FEA in an iterative design loop to optimize motor performance.
Description: Hands-on demonstration or walkthrough of a complete machine design project.
Description: Finalizing the design project, post-processing results, and generating reports.
Description: Summary of the course concepts and a look at future trends in electromagnetic simulation.
Description: Closing remarks and final Q&A on FEA applications in industry.